Question
5. \( 4 p^{3}-2 p-p q^{2}+q \) 6. \( 6 m m^{2}-2 m n-3 m p+n p \)
Ask by Alexander Moran. in South Africa
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Simplify the expressions:
1. \(4p^{3}-2p-pq^{2}+q\)
2. \(6m^{3}-2mn-3mp+np\)
Solution
Calculate or simplify the expression \( 4p^3-2p-pq^2+q \).
Simplify the expression by following steps:
- step0: Solution:
\(4p^{3}-2p-pq^{2}+q\)
Calculate or simplify the expression \( 6mm^2-2mn-3mp+np \).
Simplify the expression by following steps:
- step0: Solution:
\(6m\times m^{2}-2mn-3mp+np\)
- step1: Multiply:
\(6m^{3}-2mn-3mp+np\)
The simplified expressions are:
1. \(4p^{3}-2p-pq^{2}+q\)
2. \(6m^{3}-2mn-3mp+np\)
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Simplify this solution Extra Insights
Let's factor the expressions to make them sparkle! For \( 4 p^{3}-2 p-p q^{2}+q \), we can rearrange it to group terms: \( 4p^3 - pq^2 - 2p + q \). Factoring by grouping, we get \( 2p(2p^2 - q^2) - 1(2p - q) \). Combining those gives us the factorized form: \( (2p - 1)(2p^2 - q^2) \). Now, for \( 6 m m^{2}-2 m n-3 m p+n p \), we can rearrange and group the first two and the last two terms: \( 6m^3 - 2mn - 3mp + np \). Factoring out common terms yields \( 2m(3m - n) - p(3m - n) \). This can be factored further as \( (3m - n)(2m - p) \). Keep those algebra skills sharp—it's all about spotting patterns and grouping!
